Honestly, I graduated in the midst of this recession (in case you are wondering--with a degree in biochemistry, from a well regarded SLAC, went to a PhD program straight out of undergrad). I don't really know how important what you majored in is. There are so many factors; prestige of school, networking, luck, etc. While certain majors are viewed by employers as "fluff" majors (like communications, business), honestly people get jobs from all kinds of majors.
Certain areas are "hot" right now--if you are a really talented tech person, especially a software engineer. However, not everyone who ended up in that profession has a CS degree. Some have math degrees, some have chemistry degrees, a couple people who are around my age don't have degrees at all. If you are a really awesome coder, that's what matters. Some less than talented people get stuck in crappy, fairly low wage IT jobs without much mobility, so if you are really good there are a lot of opportunities, if not there aren't. Getting a CS degree isn't going to guarantee a good job. Also if you are a woman, there are a lot of cultural issues that people this field is working out in terms of sexism that won't be apparent until you are out of school and in the workforce, so you have to have a really thick skin.
Then there is engineering. If you are a good engineer, you can get a job and the wages are definitely high for entry level. There are also desirable non-traditional engineering opportunities (patent agent, consulting, etc.) where there is a shortage of qualified people. However, this seems to be almost exclusively true for electrical engineers. Petroleum engineers are also in high demand currently, but only a handful of schools offer that major (for example, go to University of Texas, get hired by an oil company, make 120K as a starting salary). I have a friend who did aerospace engineering who searched for over a year after he graduated for a job, and got a consulting job which he hates, but he's clinging onto it because he feels lucky to have found a job at all. For the top talent, there are certainly high paying jobs, but a lot of companies have an arbitrary GPA cutoff of 3.5. The curves in engineering are brutal, so you need to be really good to get over a 3.5. I guess what I'm saying is that it's no magic bullet. Also a lot of people need at least a masters to see the room for career growth that they really want.
Then there is applied math. I think this is often overlooked, because there are a lot of jobs as analysts, actuaries, etc. that pay really well and are in high demand. You need to be a certain sort of person to not find this work mind numbingly boring, and bright enough to pass the actuary exams, if that's what you want to do. I have a friend who went to Stanford business school after a few years working as an actuary, and she's doing really well. I think math is a great area for people who are interested in business.
Economics is hit and miss. The people who get good jobs or are qualified to go to grad school tend to have a math heavy background in economics. Coming from a good school, I think you can do really well with an economics major; coming from a less well regarded program, or being less adamant about networking, perhaps not.
Physics, biology, chemistry, and the non-engineering natural and physical sciences...sometimes I don't know why this gets included in the "STEM" acronym. One advantage coming out of undergrad is that you can pretty much get a job paying 30K plus benefits as a lab technician in chemistry/biochemistry/biology and won't need to work as a barista to pay the bills. Sometimes you can get an industry job paying a little more, like 40K. But honestly, to really advance in your career much past the 30K mark, most of the time you need to go to graduate school. Then the job market is abysmal. Think the job market for lawyers...totally bimodal. You might have a nice career in industry, consulting, whatever (or the academic job market, which is another beast in and of itself), but a lot of people get stuck after a decade of higher education working as a postdoc for 40K indefinitely. It's pretty bleak. Again, if you are really good, you'll find a way, or figure out other careers at varying points, but I think you have to hustle just as much as the humanities folks to get into a good career path with a lot of room for growth.
Business. Honestly, I think this is largely a waste. The really talented people who go to MBA programs often have degrees in math, english, really a whole range of areas. A lot of bro-y types who want an easy major go into this.
Humanities the social sciences...well this is entirely dependent on the school and the person. You won't have a career path handed to you, that's for sure. A lot of people end up unemployed or under employed (working in the service industry, etc.). But among my high achieving friends, some went to grad and professional school, and others seem to have found career paths that are fulfilling. Some have become teachers. I personally know people who have steady work with just a BA who work in journalism (one worked her way up to being an editor), marketing, publishing, for a hedge fund, management consulting, and in a variety of corporate jobs (curriculum development, analyst, etc.) The thing in common with all these people? They were complete self-starters and got lucky. But the kids who graduated Phi Beta Kappa with an English degree are often doing better than the slacker math majors, I've gotta say.
Nursing--definitely job stability here. Maybe not as "prestigious" as some other paths, but often overlooked. A smart area to go into.
Then after undergrad:
Medicine--very competitive to get into med school, period (I'm not just talking about Harvard, but getting in anywhere, and once you are in, passing your boards and so on--it's very stressful), but IMHO a very smart move. One of the few career paths left that offers a real guarantee of a comfortable salary and room for career growth. I was turned off by the obnoxious pre-med culture as an undergrad and the grade grubbing of some kids who wanted to go to med school. I was also strongly encouraged to go into a research science career from some professors. In retrospect, that would have been smart, though. Need to be very focused as an undergrad.
Law--again, bimodal. If you go to a top 10 school and graduate in the top of your class, you might get a Big Law job. Otherwise, as is talked about on this forum, the prospects are pretty bleak.
PhD: let's not even go into the problems with the academic job market.
various masters: sometimes necessary, sometimes a waste of time. Often depends on networking.
MBA: only useful if from a top school for networking
My take away? If you get good grades are super focused AND/OR network like mad and really hustle and are in the top 10% of people who graduate from college in an area you are good at, you'll probably be fine. If not? Good luck. But in any case, you're better off than people without a degree, because at least when you actually make it to an interview, HR won't screen you out. And a lot of networking happens in college. But at least you'll be making 30K+ rather than minimum wage.